Transparent Corp's Research Area is arguably the most comprehensive resource for collated brainwave entrainment research. Update: the main research area on Transparent Corp's website is currently being updated, so it is offline. However, you can still access their peer-reviewed research paper as a PDF here: “A Comprehensive Review of the Psychological Effects of Brainwave Entrainment“.
Because the mind and body are a single system, changing our brainwaves and spending more time in harmonious, relaxed, and restorative mind-states also affects our physical health. Physical health then reinforces our mental-state, and a feedback loop of either positive or negative processes becomes established. Research studies have shown beneficial effects of using brainwave entrainment for treating migraine headaches, premenstrual syndrome, and for managing physical pain.
There is a lot to like about this technology as a potential treatment for sleep problems. It’s low impact and non-invasive, it doesn’t rely on chemical drugs, it’s inexpensive and for most people likely easy to adopt and maintain. In this way, it’s similar to the other behavioral therapies for sleep that I like so much, including meditation and relaxation techniques, and other mind-body therapies.
Both brainwave entrainment and neurofeedback deal with brainwaves, but the similarity stops there. Entrainment pushes your whole brain into a pre-determined state, while neurofeedback teaches you how to move specific parts of your brain on your own. It is the differeence between forcing the brain into a given position, and skills building so you can move it there yourself.